Tension control in actuation of multi-joint medical instruments

ABSTRACT

Control systems and methods for a medical instrument use measurements to determine and control the tensions that actuators apply through instrument transmission systems. The use of tension and feedback allows control of a medical instrument having transmission systems that provide non-negligible compliance between joints and actuators even when the positions of joints cannot be directly related to actuator positions. One embodiment determines joint torques and tensions from differences between desired and measured joint positions. Another embodiment determines joint torques and tensions from differences between desired and measured positions of a tip of the instrument. Determination of tensions from joint torques can be performed using sequential evaluation of joints in an order from a distal end of the instrument toward a proximal end of the instrument.

BACKGROUND

Minimally invasive medical procedures often employ instruments that arecontrolled with the aid of a computer or through a computer interface.FIG. 1, for example, shows a robotically controlled instrument 100having a structure that is simplified to illustrate basic workingprinciples of some current robotically controlled medical instruments.(As used herein, the terms “robot” or “robotically” and the like includeteleoperation or telerobotic aspects.) Instrument 100 includes a tool orend effector 110 at the distal end of an elongated shaft or main tube120. In the illustrated example, end effector 110 is a jawed tool suchas forceps or scissors having separate jaws 112 and 114, and at leastjaw 112 is movable to open or close relative to jaw 114. In use during amedical procedure, end effector 110 on the distal end of main tube 120may be inserted through a small incision in a patient and positioned ata work site within the patient. Jaws 112 may then be opened and closed,for example, during performance of surgical tasks, and accordingly mustbe precisely controlled to perform only the desired movements. Apractical medical instrument will, in general, require many degrees offreedom of movement in addition to opening and closing of jaws 112 and114 in order to perform a medical procedure.

The proximal end of main tube 120 attaches to a transmission or drivemechanism 130 that is sometimes referred to as backend mechanism 130.Tendons 122 and 124, which may be stranded cables, rods, tubes, orcombinations of such structures, run from backend mechanism 130 throughmain tube 120 and attach to end effector 110. A typical surgicalinstrument would also include additional tendons (not shown) thatconnect backend mechanism 130 to other actuated members of end effector110, a wrist mechanism (not shown), or actuated vertebrae in main tube120, so that backend mechanism 130 can manipulate the tendons to operateend effector 110 and/or other actuated elements of instrument 100. FIG.1 illustrates jaw 112 as having a pin joint structure 116 that providesa single degree of freedom for movement of jaw 112. Two tendons 122 and124 are attached to jaw 112 and to a pulley 132 in backend mechanism130, so that rotations of pulley 132 cause jaw 112 to rotate.

Pulley 132 is attached to a drive motor 140, which may be at the end ofa mechanical arm (not shown), and a control system 150 electricallycontrols drive motor 140. Control system 150 generally includes acomputing system along with suitable software, firmware, and peripheralhardware. Among other functions, control system 150 generally provides asurgeon or other system operator with an image (e.g., a stereoscopicview) of the work site and end effector 110 and provides a controldevice or manipulator that the surgeon can operate to control themovement of end effector 110. The software or firmware needed forinterpretation of user manipulations of the control device and forgeneration of the motor signals that cause the corresponding movement ofjaw 112 are generally complex in a real robotic medical instrument. Toconsider one part of the control task, the generation of the controlsignals for drive motor 140 commonly employs the relationship betweenthe angle or position of jaw 112 and the angle or position of drivemotor 140 or pulley 132 in backend mechanism 130. If the tendons 122 and124 are rigid (e.g., if stretching of tendons is negligible), controlsystem 150 can use a direct relationship between the angular position ofdrive motor 140 and the angular position of jaw 112 as defined by thegeometry of instrument 100 in determining the control signals needed tomove jaw 112 as a surgeon directs. Minor stretching of tendons 122 and124, for example, under a working load, can be handled by somemathematical models relating motor position to effector position.However, if the mechanical structure including end effector 110, tendons122 and 124, and backend mechanism 130 has a high degree of compliance,a relationship between the angular position of motor 140 (or pulley 132)and the angular position of jaw 112 may be difficult or impossible tomodel with sufficient accuracy for a medical instrument. Accordingly,such systems require control processes that do not rely on a fixedrelationship between the applied actuator control signals and theposition of the actuated elements.

It should be noted that in the following, the joint of the medicalinstrument can be a pin joint structure or a structure that provides oneor more degrees of freedom of motion to the instrument tip. For instancea joint can be a continuously flexible section or a combination of pinjoints that approximates a continuously flexible section or a singlerotary joint that is not purely revolute but provides also some rollingjoint. See, for example, U.S. Pat. No. 7,320,700, by Cooper et Al.,entitled “Flexible Wrist for Surgical Tool,” and U.S. Pat. No.6,817,974, by Cooper et Al., entitled “Surgical Tool Having a PositivelyPositionable Tendon-Actuated Multi-disk Wrist Joint.”

It should also be noted that in the state of the art of control ofmedical robotic instruments, the actuator positions are servo controlledto produce the desired instrument tip motion or position. Such anapproach is effective as long as the transmission systems between theactuators and the instrument joints are rigid for all practicalpurposes. See, for example, U.S. Pat. No. 6,424,885, entitled “CameraReferenced Control in a Minimally Invasive Surgical Apparatus.” Such anapproach can also be effective if the flexibility of the transmissionsystem can be modeled exactly and a model included in the controller asdescribed in U.S. Pat. App. Pub. No. 2009/0012533 Al, entitled “RoboticInstrument Control System” by Barbagli et Al.

SUMMARY

In accordance with an aspect of the invention, control systems andmethods for an instrument having multiple degrees of freedom usedifferences between a current configuration/velocity of the instrumentand a desired configuration/velocity of the instrument to determine andcontrol the forces that proximal actuators apply to the instrumentthrough a set of transmission systems. The use of applied force andfeedback indicating the resulting configuration of a medical instrumentallows robotic control of the medical instrument, even if transmissionsystems of the instrument have non-negligible compliance between theproximal actuators and remote actuated elements. The feedback approachparticularly allows precise instrument operation even when theconfiguration of the instrument cannot be directly inferred from thepositions of the proximal actuators.

In one embodiment of the invention, the configuration of an end effectoror tip is measured or otherwise determined, and the differences betweenthe current and desired configurations of the tip are employed indetermining the required joint torques and the applied forces needed toachieve the desired tip configuration. Embodiments of this controlmethod can allow selection of the dynamic behavior of the tip, forexample, to facilitate the instrument interaction with tissue, whilepermitting flexibility in other portions of the instrument.

In another embodiment of the invention, the configuration of each jointin an instrument is measured, and the differences between current anddesired joint configurations are used to determine the actuator forcesneeded to move all of the joints to desired configurations.

One specific embodiment of the invention is a medical system thatincludes multiple joints, actuators, and transmission systems. Thetransmission systems have proximal ends respectively coupled to theactuators, and each of the transmission systems has a distal endattached to an associated one of the joints to allow the transmission ofa force for articulation of the associated joint. A sensor in themedical system measures configuration of the joints or the instrumenttip, and a control system that operates the actuators to apply forces tothe transmission systems, receives the configuration measurements fromthe sensor and uses the configuration measurements to determine theactuation forces applied to the transmission systems.

Another specific embodiment of the invention is a method for controllinga medical instrument. The method includes: measuring a configuration fora plurality of joints of the medical instrument; receiving a commandindicating a desired configuration of the medical instrument;determining tensions respectively in transmission systems that connectrespective actuators to the joints, and operating the actuator to applythe forces respectively to the transmission systems. The determinationof the applied forces is independent of positions of the actuators.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates features of a known robotically controlled medicalinstrument.

FIG. 2 illustrates a medical instrument that can be operated using acontrol process in accordance with an embodiment of the invention thatcontrols the force applied through a compliant transmission system tocontrol an articulated vertebra of the instrument.

FIG. 3A illustrates a medical instrument in which a control process inaccordance with an embodiment of the invention can operate with atransmission system having minimum and maximum force transfer to operatea mechanical joint.

FIG. 3B shows an embodiment of the invention in which a joint includescontinuously flexible structure.

FIG. 3C illustrates positions of a pair of tendons used to control asingle degree of freedom of motion in the joint of FIG. 3B.

FIG. 4 schematically illustrates a robotic medical system andparticularly shows quantities used in an embodiment of the inventionthat controls a remote joint connected to actuators through complianttransmission systems.

FIG. 5A is a flow diagram of a control process in accordance with anembodiment of the invention.

FIG. 5B is a flow diagram of a process for determining a tensioncorrection associated with a difference between an actuator velocity anda joint velocity.

FIG. 5C is a flow diagram of a process for determining a tensioncorrection associated with a difference between the velocities ofactuators manipulating the same joint.

FIG. 5D illustrates a function for control of a maximum and minimumapplied tension.

FIG. 6 schematically illustrates a robotic medical system andparticularly shows quantities used in an embodiment of the inventionthat controls a multi jointed instrument.

FIG. 7A is a flow diagram of a process in accordance with an embodimentof the invention that selects applied tensions based on differencesbetween measured and desired joint configurations.

FIG. 7B is a flow diagram of a process in accordance with an embodimentof the invention that selects applied tensions based on differencesbetween measured and desired tip configurations.

FIG. 8A is a side view of a portion of a multi jointed instrument thatcan be operated using drive force control in accordance of an embodimentof the invention to control joints with parallel actuation axes.

FIGS. 8B and 8C respectively show side and end views of a portion of amulti jointed instrument having joints with perpendicular actuation axesthat can be operated using drive force control in accordance with anembodiment of the invention.

FIG. 9A shows an embodiment of the invention in which a joint includes acontinuously flexible structure that provides two degrees of freedom ofmotion.

FIGS. 9B and 9C illustrate embodiments of the invention respectivelyemploying four and three tendons to control two degrees of freedom ofmotion in the joint of FIG. 9A.

FIG. 9D shows an embodiment of a two jointed medical instrument in whicheach joint includes a continuously flexible structure and provides twodegrees of freedom of motion.

FIG. 9E illustrates an embodiment of the invention employing six tendonsto control four degrees of freedom of motion provided by the two jointsin the instrument of FIG. 9D.

FIG. 10 is a flow diagram illustrating a process in accordance with anembodiment of the invention that determines tensions through sequentialevaluation of joints in a multi jointed instrument.

Use of the same reference symbols in different figures indicates similaror identical items.

DETAILED DESCRIPTION

In accordance with an aspect of the invention, a medical instrument canbe controlled via transmission systems that do not provide fixedrelationships between actuator positions and joint positions. Inparticular, the actions of a system operator (e.g., a surgeon) canindicate a currently desired configuration/velocity for the medicalinstrument, while a sensor measures the actual configuration/velocity ofthe instrument. Forces, tensions, or torques can then be selectedaccording to the desired and measured configurations and applied throughthe transmission systems to move the instrument toward its desiredconfiguration. The selection criteria for the applied force, tension, ortorque can be altered if prior selections of the applied force, tension,or torque resulted in the joint overshooting or failing to reach adesired position.

FIG. 2 illustrates a portion of a compliant medical instrument 200having a transmission system such as described by U.S. patentapplication Ser. No. 12/494,797, entitled “Compliant Surgical Device,”which is hereby incorporated by reference in its entirety. Instrument200 includes a jointed element 210 that is manipulated through controlof the respective tensions in tendons 222 and 224. In general,instrument 200 may contain many mechanical joints similar to jointedelement 210, and each joint may be controlled using tendons similar totendons 222 and 224. In an exemplary embodiment, instrument 200 is anentry guide that can be manipulated to follow a natural lumen within apatient. An entry guide would typically include a flexible outer sheath(not shown) that surrounds vertebrae (including element 210) and provideone or more central lumens through which other medical instruments canbe inserted for access to a work site. Compliance is particularlydesirable in entry guides to prevent an action or reaction of the entryguide from harming surrounding tissue that may move or press against theentry guide. However, other types of medical instruments may alsobenefit from compliant drive mechanisms of the type illustrated in FIG.2.

Instrument 200 includes a backend mechanism 230 that with tendons 222and 224 provides a compliant transmission system connecting to jointedelement 210 to drive motors 242 and 244. In particular, backendmechanism 230 includes spring systems 235 attached to tendons 222 and224 and drive motors 242 and 244. Each spring system 235 in FIG. 2includes a mechanical drive system 232 and a constant force spring 234.Each drive system 232 couples a motor 242 or 244 and converts rotationalmotion of the drive motor 242 or 244 into linear motion that changes theconstant force applied by the associated constant force spring 234 totendon 222 or 224. In the illustrated embodiment, each constant forcespring 234 includes a conventional Hooke's law spring 236 and a cam 238.Each spring 236 connects to an associated drive system 232 so that thelinear motion of drive system 232 moves a proximal end of the spring236. Each cam 238 has a first guide surface on which a cable 237attached to the distal end of the associated spring 236 attaches andrides and a second guide surface on which a portion of tendon 222 or 224attaches and rides. The guide surfaces of each cam 238 generally providedifferent moment arms for the action of the attached cable 237 and theattached tendon 222 or 224 and are shaped so that the tension in tendon222 or 224 remains constant as the paying out or hauling in of a lengthof tendon 220 or 224 changes the force applied by the attached spring236. Each surface of each cam 238 may be a spiral surface that extendsfor one or more revolutions in order to provide the desired range ofmovement of the tendon 222 and 224 while maintaining a constant tensionin tendon 222 or 224.

Each drive system 232 controls the position of the proximal end of thecorresponding spring 236 and thereby influences the amount of baselinestretch in the corresponding spring 236 and the tension in the attachedtendon 222 or 224. In operation, if a drive system 232 in a springsystem 235 pulls on the attached spring 236, the spring 236 begins tostretch, and if the element 210 and tendon 222 or 224 attached to thespring system 235 are held fixed, the force that spring 236 applies tocam 238 increases and therefore the tension in the attached cable 222 or224 increases. Accordingly, the tensions in tendons 222 and 224 dependlinearly (in accordance with Hooke's law, the moment arms of cam 238,and the spring constant of spring 236) on movement of the proximal endsof respective springs 236, but each spring system 235 behavesasymmetrically, i.e., acts with constant force in response to externalor distal forces that move tendon 222 or 224. Constant force spring 234and drive system 232 can be alternatively implemented in a variety ofways such as those described further in above-referenced U.S. patentapplication Ser. No. 12/494,797.

Jointed element 210 has a single degree of freedom of motion (e.g.,rotation about an axis) and generally moves when drive motor 242 or 244rotates a drive system 232 to change the force applied by the attachedconstant force spring 238. However, this drive mechanism is compliant sothat external forces can move element 210 without a correspondingrotation of drive system 232. As a result, there is no fixedrelationship between the position or orientation of jointed element 210and the position of drive system 232 or drive motor 242. In accordancewith an aspect of the invention, control system 250 uses a sensor 260 tomeasure the orientation of element 210. Sensor 260 may be, for example,a shape sensor, which can sense the shape of jointed element 210 along alength of instrument 200 including element 210. Some examples of shapesensors are described in U.S. Pat. App. Pub. No. US 2007/0156019 Al(filed Jul. 20, 2006), entitled “Robotic Surgery System IncludingPosition Sensors Using Fiber Bragg Gratings” by Larkin et al., and U.S.patent application Ser. No. 12/164,829 (filed Jun. 30, 2008) entitled“Fiber optic shape sensor” by Giuseppe M. Prisco, both of which areincorporated herein by reference. However, any sensor capable ofmeasuring an angular position of jointed element 210 could alternativelybe used. A control process as described further below uses suchmeasurements for calculation of applied forces needed to manipulatejointed element 210.

Instrument 200 has “backdriving” capability when backend mechanism 230is detached from a motor pack, constant force springs 235 still keeptendons 222 and 224 from slacking and allow the distal portion ofinstrument to be manually arranged (or posed) without damaging backendmechanism 230 or creating slack in tendon 222 or 224. This “backdriving”capability is generally a desirable property of a surgical instrument,particularly an instrument with a flexible main tube that may be bent ormanipulated during instrument insertion while the instrument is notunder active control by control system 250. For example, instrument 200can be manually posed, and the tendons within the main shaft do notexperience undue tension or slack.

Another example of a compliant transmission system for a joint in amedical instrument is illustrated in FIG. 3A. FIG. 3A shows an exemplaryembodiment of a medical instrument 300 that uses an actuation processthat permits a drive motor to freewheel or a drive tendon to sliprelative to the drive motor during instrument operation as described inU.S. patent application Ser. No. 12/286,644, entitled “Passive Preloadand Capstan Drive for Surgical Instruments,” which is herebyincorporated by reference in its entirety. Medical instrument 300 has anend effector 310 at the end of a main tube 320, and a backend mechanism330 manipulates tendons 322 and 324, which run through main tube 320, tocontrol a degree of freedom of motion of end effector 310. In theillustrated embodiment, tendons 322 and 324 attach to a mechanicalmember in end effector 310 such that tensions in tendons 322 and 324tend to cause end effector 310 to rotate in opposite directions about apivot joint structure.

The joint structure of FIG. 3A is only an example, and other jointmechanisms that provide a single degree of freedom of motion in responseto tensions applied to a pair of tendons could be employed inalternative embodiments of the invention. FIG. 3B, for example,illustrates an embodiment in which joint 310 such as commonly found incatheters, endoscopes for the gastrointestinal tract, the colon, and thebronchia; guide wires; or other endoscopic instruments such as graspersand needles used for tissue sampling.

that is able to flex or bend in response to forces applied throughtendons 322 and 324. The catheter joint may simply include an extrusionof a plastic material that bends in response to a differential in thetension in tendons 322 and 324. In one configuration, tendons 322 and324 extend through lumens within the catheter and attach to the end ofthe catheter as shown in FIG. 3C. Accordingly, the forces in tendons 322and 324 can be used to bend the catheter in the direction correspondingto the tendon 322 or 324 having greater tension. Bending of the cathetermay be used, for example, to steer the catheter during insertion. In theembodiment of FIG. 3B, distal sensor 360 can measure the bend angle ofthe distal portion of the catheter to measure or compute the “joint”angle and velocity. In one particular embodiment, the bend angle can bedefined as a tip orientation of the catheter with respect to the base ofthe distal flexible portion of the catheter. The backend and controlarchitecture for catheter joint 310 of FIG. 3B can be identical to thatof the embodiment of FIG. 3A, except that the measured joint angle andvelocity can be converted to tendon position and velocity bymultiplication of the distance between the actuator cable lumen and thecenter of the distal flexible portion.

Backend mechanism 330, which attaches to the proximal end of main tube320, acts as a transmission that converts torques applied by drivemotors 342 and 344 into tensions in respective tendons 322 and 324 andforces or torques applied to an actuated joint in end effector 310. Inthe illustrated embodiment, drive motors 342 and 344 can be direct driveelectrical motors that directly couple to capstan 332 and 334 aroundwhich respective tendons 322 and 324 wrap. In particular, tendon 322wraps for a set wrapping angle (that could be less than a full turn oras large as one or more turns) around the corresponding capstan 332 andhas an end that is not affixed to capstan 332 but extends from thecapstan 332 to a passive preload system 333. Similarly, tendon 324 wrapsfor a set wrapping angle around the corresponding capstan 334 and has anend extending from the capstan 334 to a passive preload system 335.Since tendons 322 and 324 are not required to be permanently attached tocapstans 332 and 334, tendon 322 and 324 may be able to slip relative tocapstans 332 and 334 and relative to the shaft of drive motors 342 and344 that respectively couple to capstans 332 and 334.

The proximal end of tendons 322 and 324 attach to respective passivepreload systems 333 and 335, each of which is implemented in FIG. 3A asa cam and a Hooke's law spring that together act as a constant forcespring. Passive preload systems 333 and 335 are biased, so that systems332 and 334 apply non-zero forces or tensions to tendons 322 and 324throughout the range of motion of instrument 300. With thisconfiguration, when capstans 332 and 334 are free to rotate, passivepreload systems 333 and 335 control the tensions in tendons 322 and 324and avoid slack in tendons 322 and 324 by pulling in or letting out therequired lengths of tendons 322 and 324. When backend mechanism 330 isdetached from motors 342 and 344, passive preload systems 333 and 335still keep tendons 322 and 324 from slacking and allow end effector 310and main tube 320 (when flexible) to be manually arranged (or posed)without damaging backend mechanism 330 or creating slack in tendon 322or 324. Accordingly, instrument 300 also has “backdriving” capabilitysimilar to that described above for instrument 200 of FIG. 2.

End effector 310 can be operated using drive motors 342 and 344 underthe active control of control system 350 and human input (e.g., mastercontrol input in a master-slave servo control system). For example, whenmotor 342 pulls on tendon 322, the motor torque is transferred as anapplied tension in the distal portion of tendon 322. (A maximum tensionthat capstan 332 can apply to proximal portion of tendon 322 depends ona tension at which tendon 322 begins to slip relative to captain 332,but in general, the maximum tension actually used can be selected toprevent tendons 322 and 324 from slipping on capstans 332 and 334.) Atthe same time, when turning off the power to motor 344, allowing motor344 and capstan 334 to freewheel, tendon 324 can be kept at its minimumtension that is the constant force that passive preload system 335applies to proximal end of tendon 324 through the capstan 334. Thelarger tension in tendon 322 then tends to cause end effector 310 torotate counterclockwise in FIG. 3A. Similarly, turning off power tomotor 342 and powering motor 344 to apply force through tendon 324 toend effector 310 tends to cause end effector 310 to rotate clockwise inFIG. 3A. The ability of motor 342 and 344 to freewheel while tendons 322and 324 are under tension and the acceptance of slippage of tendons 322and 324 on capstans 332 and 334 do not permit control system 350 to relyon a fixed relationship between the angular positions of motor 340 andend effector 310. However, control system 350 can use a sensor 360 tomeasure the angular position of end effector 310 relative to the jointactuated through tendons 322 and 324.

The instruments of FIGS. 2, 3A, and 3B may have transmission systemsbetween actuators and actuated joints provide compliance that isdesirable, particularly for instruments with a flexible main tube.However, transmission systems with compliance may also occur in moretraditional instruments. For example, the known instrument of FIG. 1 mayuse sheathed or Bowden cables in sections of the instrument that bendand rod elements in straight sections. The rod elements can reducestretching that interferes with the direct relationship of actuator andjoint positions. However, it may be desirable in some applications touse tendons of more flexible material (e.g., polymer tendons whereelectrical insulation or minimal friction is desired), but such tendonsmay introduce an unacceptable amount of stretch for control processesrelying on a direct relationship between actuator and joint position.Solid steel pull wires can also be used in or as transmission systems.

In accordance with an aspect of the current invention, control processesfor the medical instruments of FIGS. 2, 3A, and 3B or instruments thatotherwise have compliant transmission systems can employ remotemeasurements of the position of a mechanical joint to determine atension to be applied to drive the mechanical joint. The controlprocesses could also be employed for instruments having rigidtransmission systems. FIG. 4 schematically shows a generalization of amedical instrument 400 having a mechanical joint 410 having a degree offreedom of motion corresponding to an angle or position θ. The termposition is used broadly herein to include the Cartesian position,angular position, or other indication of the configuration of a degreeof freedom of a mechanical system. A sensor (not shown) measuresposition θ at the remote joint 410 and provides measured position θ to acontrol system 450, for example, through a signal wire (not shown)extending from the sensor at the distal end of instrument 400, throughthe main tube (not shown) of instrument 400 to control system 450 at theproximal end of the instrument. The sensor may additionally measure avelocity {dot over (θ)} for the movement of joint 410, or velocity {dotover (θ)} may be determined from two or more measurements of position θand the time between the measurements.

Joint 410 is connected through a transmission system 420 to an actuator440, so that joint 410 is remote from actuator 440, e.g., joint 410 maybe at a distal end of the instrument while actuator 440 is at theproximal end of the instrument. In the illustrated embodiment,transmission system 420 connects joint 410 so that a tension T appliedby actuator 440 to transmission system 420 tends to rotate joint 410 ina clockwise direction. In general, transmission system 420 includes theentire mechanism used to transfer force from actuator 440 to joint 410,and actuator 440 may apply a force or torque to transmission system 420which results in a tension in a cable or other component of transmissionsystem 420. However, such a tension is generally proportional to theapplied force or torque, so the term tension is intended to be used herewithout loss of generality to also indicate force or torque. It shouldalso be noted that transmission system 420 may be (but is not requiredto be) so compliant that a direct relationship between the position ofjoint 410 and the position of actuator 440 would not be accurate enoughfor control of joint 410. For example, transmission system 420 maystretch, so that between a minimum and a maximum of tension T applied totransmission system 420, the difference in the effective length oftransmission system 420 may correspond to 45° of joint articulation. Incontrast, a typical medical device allows for stretching thatcorresponds to no more than a few degrees of joint articulation in orderto be able to accurately model the position of the joint based onactuator position. It should be understood that in the general casecompliance is not limited to a simple Hooke's law stretching of a springstructure. Transmission system 420 may include, for example, tendon 222and at least a portion of backend mechanism 230 in the embodiment ofFIG. 2 or tendon 322 and at least a portion of backend mechanism 330 inthe embodiment of FIG. 3A. In general, the response of transmissionsystem 420 to a tension T applied at a proximal end of transmissionsystem 420 and to external forces applied to joint 410 or along thelength of transmission system 420 may be difficult to model.

Actuator 440, which can include drive motor 242 or 342 of FIG. 2 or 3A,applies tension T to the proximal end of transmission system 420 andthrough transmission system 420 applies force or torque to joint 410,but other forces and torques are also applied to joint 410. Inparticular, one or more other transmission systems 420 may be connectedto joint 410 and collectively apply a net tension or force that tends tocause joint 410 to rotate. In the illustrated embodiment of FIG. 4, atransmission system 422 is connected to joint 410 and to a drive motor442, so that tension in transmission system 422 tends to oppose appliedtension T and rotate joint 410 counterclockwise in FIG. 4. Theadditional transmission system 422 or transmission systems connected tojoint 410 may be the same as transmission system 420, other than adifference in where the transmission systems 422 connect to joint 410.

Control system 450 can be a general purpose computer executing a programor a circuit wired to generate a drive signal that controls a tension Tthat actuator 440 applies to transmission system 420. When actuator 440is an electrical motor, the drive signal may be a drive voltage orcurrent that controls the torque output from actuator 440, and tension Tis equal to the motor torque divided by the effective moment arm atwhich tension T is applied to transmission system 420. As describedfurther below, control system 450 can calculate the magnitude of tensionT or the motor torque using a desired position θ_(D), a desired velocity{dot over (θ)}_(D) for joint 410, and one or more measurements ofposition θ for joint 410 at the current and prior times. A user (e.g., asurgeon controlling system 400) can provide desired position θ_(D) andvelocity {dot over (θ)}_(D) by manipulating a controller 460. The exactconfiguration of controller 460 is not critical to the present inventionexcept that controller 460 is able to provide signals from which valuesfor the desired position θ_(D) and velocity {dot over (θ)}_(D) can bedetermined. Manual controllers suitable for complex medical instrumentsgenerally provide signals that indicate many simultaneous instructionsfor movements of the medical instrument, and such movements may involvemultiple joints in the instrument. Suitable manipulators for use ascontroller 460 are provided, for example, in the master controller ofthe da Vinci Surgical System available from Intuitive Surgical, Inc.

The tension T needed to move joint 410 from its current measuredposition θ to desired position θ_(D) in a time interval Δt willgenerally depend on many factors including: the effective inertia ofjoint 410 that resists applied tension T; the inertia of actuator 440which applies tension T, any other transmission systems 422 coupled tojoint 410 and applying a net effective force; external forces applied tojoint 410; internal and external frictional forces that oppose actuationof joint 410 or movement of transmission system; the current velocity{dot over (θ)} of joint 410; and internal and external damping forces.Many of these factors may vary depending on the working environment ofinstrument 400 and may be difficult to measure or model. However, modelscan be developed based on system mechanics or empirically for aparticular joint in a medical instrument. In one specific embodiment,control system 450 determines the tension T from the distal joint errors(θ_(D)−θ) and ({dot over (θ)}_(D)−{dot over (θ)}), which arerespectively the difference between the measured and desired positionsof joint 410 and the difference between measured and desired velocitiesof joint 410.

FIG. 5A is a flow diagram of a process 500 for controlling a medicalinstrument having the basic structure of system 400 of FIG. 4. Process500 begins in step 510 by reading a current value of position θ of joint410 and determining a current value for the joint velocity {dot over(θ)}. Velocity {dot over (θ)} can be directly measured or determined orapproximated in a well known manner using the current position θ, aprior position θ′, a time interval Δt between measurements, for example,under the assumption of constant velocity (e.g., {dot over(θ)}=(θ−θ′)/Δt) or under the assumption of constant acceleration given aprior determination of velocity. Step 515 then acquires a desiredposition θ_(D) and a desired velocity {dot over (θ)}_(D) for joint 410,and step 520 computes a difference or error (θ_(D)−θ) between themeasured and desired positions and a difference or error ({dot over(θ)}_(D)−{dot over (θ)}) between the measured and desired velocities.

The position and velocity error computed in step 520 can be used todetermine tension T required for joint 410 to reach the desired positionθ_(D). In the embodiment of FIG. 5A, applied tension T may includemultiple contributions, and the primary contribution is a distal tensionT_(DIST), which is determined as a function f₁ of position error(θ_(D)−θ) and velocity error ({dot over (θ)}_(D)−{dot over (θ)}). Distaltension T_(DIST) is independent of the position of the actuator, e.g.,of the angle of the motor shaft, which allows determination of distaltension T_(DIST) even when there is no direct relationship between theposition of joint 410 and the position of actuator 440. In oneparticular embodiment, the function f₁ is of the form Equation 1, whereg1 and g2 are gain factors, C is a constant or geometry dependentparameter, and T_(sign) is a sign, i.e., ±1. Sign T_(sign) is associatedwith movement of joint 410 produced by tension in transmission system420 and may, for example, be positive (e.g., +1) if tension T intransmission system 420 tends to increase the position coordinate θ andnegative (e.g., −1) if tension T in transmission system 420 tends todecrease the position coordinate θ. In another embodiment, function f₁imposes a lower bound on the force, for instance, in order for the forceto be always positive and sufficient to avoid slack in the transmissionsystem. The parameter C can be a constant selected according to known ormodeled forces applied to joint 410 by other portions of the system. Forexample, parameter C may be a constant selected to balance the torquecaused by other transmission systems applying force to joint 410 or mayaccount for expected friction or external forces. However, parameter Cis not required to strictly be a constant but could include non-constantterms that compensate for properties such as gravity or mechanismstiffness that can be effectively modeled, and accordingly, parameter Cmay depend on the measured joint position or velocity. The gain factorsg1 and g2 can be selected according to the desired stiffness anddampening of joint 410. In particular, when joint 410 is used as astatic grip, the net gripping force or torque applied to tissue dependson the term g1(θ_(D)−θ) of Equation 1. In general, gain factors g1 andg2 and constant C can be selected according to the desired stiffness anddampening or responsiveness of joint 410 or according to an accumulationof error. For example, when inserting the instrument 400 to follow anatural lumen within a patient, the gain factor g1 can be set to a lowvalue to make joint 410 behave gently and prevent joint 410 from harmingsurrounding tissue. After the insertion, the gain factor g1 can be setto a higher value that allows the surgeon to perform precise surgicaltask with the instrument.

F ₁ =T _(sign)*(g1(θ_(D)−θ)+g2({dot over (θ)}_(D)−{dot over(θ)})+C)  Equation 1

The term g1(θ_(D)−θ)+g2({dot over (θ)}_(D)−{dot over (θ)})+C of Equation1 can be used to approximately determine the torque, tension, or forcecurrently required at joint 410 to rotate joint 410 to reach the desiredposition θ_(D) using transmission system 420 in a given time Δt. Thetorque and force or tension are related in that the torque is theproduct of the force and an effective movement arm R, which is definedby the perpendicular distance between the connection of transmissionsystem 420 to joint 410 and the rotation axis of joint 410. Theeffective movement arm R can either be absorbed into gain factors g1 andg2 and constant C or used to convert a calculated distal tensionT_(DIST) into a calculated torque.

Distal tension T_(DIST), with the proper choice of function f₁, e.g.,proper selection of parameters g1, g2, and C in Equation 1, canapproximate the force that actuator 440 is required to apply to movejoint 410 in a manner that is responsive to manipulations by a humanoperator of manual controller 460. However, optional corrections areprovided by steps 530, 535, 540, and 545 under some conditions. Inparticular, optional steps 530 and 535 respectively compute a saturatedsum or integral I of the position error (θ_(D)−θ) and calculate anintegral tension T_(INT). The integral tension T_(INT), which may bepositive, zero, or negative, can be added as a correction to distaltension T_(DIST), which was calculated in step 525. Integral tensionT_(INT) is calculated as a function f₂ of saturated integral I and maysimply be the product of integral I and a gain factor. The saturatedintegral I calculated in step 530 can simply be the sum for the past Nintervals of position errors (θ_(D)−θ) or differences (θ_(D,i)−θ_(i-1))between the measured position at the end of the interval and the desiredposition that was to be achieved. The number N of intervals involved inthe sum may be limited or not, and integral I may be saturated in thatthe magnitude of the integral is not permitted to exceed a maximumsaturation value. The saturation value would generally be selected tocap the maximum or minimum value of integral tension T_(INT). However,the minimum and maximum values of integral tension T_(INT) canalternatively be capped when calculating the value of function f₂.

Optional step 540 computes another correction referred to herein asproximal tension T_(PROX), which may be positive, zero, or negative.Proximal tension T_(PROX) can be added to distal tension T_(DIST), whichwas calculated in step 525. FIG. 5B is a flow diagram of a process 540for computing proximal tension T_(PROX). Process 540 begins in step 542by reading a current value of a velocity {dot over (θ)}_(A) of actuator440. Velocity {dot over (θ)}_(A) can be measured by a standardtachometer that attaches at the base of actuator 440. To improvecomputational efficiency, step 542 can also be scheduled to run betweensteps 510 and 515 of FIG. 5A. Step 544 then computes the proximalvelocity difference or error ė_(PROX), which is defined as thedifference or error between a desired velocity computed based on desiredvelocity {dot over (θ)}_(D) of joint 410 and the current velocitycomputed based on the current actuator velocity {dot over (θ)}_(A). Inone particular embodiment, the desired velocity can be the product ofthe effective moment arm R, sign T_(sign), and desired velocity {dotover (θ)}_(D) of joint 410, while the current velocity can be theproduct of an effective moment arm of the actuator 440 and actuatorvelocity {dot over (θ)}_(A). In the embodiment of FIG. 5B, proximaltension T_(PROX) is determined as a function f₄ of proximal velocityerror ė_(PROX). In one particular embodiment, the function f₄ may simplybe the product of proximal velocity error ė_(PROX) and a gain factor.The gain factor can be selected to provide an additional dampeningeffect to transmission system 420.

Optional step 550 of FIG. 5A computes a pair tension T_(PAIR), which maybe positive, zero, or negative correction to distal tension T_(DIST),which was calculated in step 525. FIG. 5C is a flow diagram of a process550 for computing the pair tension T_(PAIR). Process 550 begins in step552 by reading a current value of velocity {dot over (θ)}₄ of actuator440 and velocity values of all other actuators associated with joint410. In the system of FIG. 4, there are two actuators 440 and 442coupled to joint 410 and two actuator velocities {dot over (θ)}_(A) and{dot over (θ)}_(A′). Step 552 can be scheduled to run between steps 510and 515 of FIG. 5A to improve computational efficiency. Step 556 thencomputes a pair velocity difference or error ė_(PAIR), which can bedefined as the difference or error between the current velocities {dotover (θ)}_(A) and {dot over (θ)}_(A′) of the actuators 440 and 442associated to joint 410, when actuators 440 and 442 are substantiallyidentical, e.g., have the same effective moment arms for operation onrespective transmission systems 420 and 422. In one particularembodiment, the current velocity error ė_(PAIR) can be the product ofthe difference ({dot over (θ)}_(A)−{dot over (θ)}_(A′)) and theeffective moment arm of actuators 440 and 442. In the embodiment of FIG.6, pair tension T_(PAIR) is determined as a function f₅ of pair velocityerror ė_(PAIR). In one particular embodiment, the function f₅ may simplybe the product of pair velocity error ė_(PAIR) and a gain factor. Thegain factor can be selected to provide additional dampening effect totransmission system 420.

Tension T is determined in step 560 of FIG. 5A as a function f₃ of sumof distal tension T_(DIST), proximal tension T_(PROX), pair tensionT_(PAIR), and integral tension T_(INT). In the embodiment of FIG. 5C,function f₃ limits the maximum and minimum values of tension T. Maximumtension T_(MAX) and minimum tension T_(MIN) can be set in theprogramming of control system 450 (e.g., in software). However, acompliant transmission system may itself have a minimum or maximumtension with proper design in the backend mechanism. For example, atransmission system illustrated in FIG. 3A has a minimum tension T_(MIN)controlled by the setting of preload system 333 or 335 whenmotor/actuator 342 or 344 is freewheeling and a maximum tension T_(MAX)resulting from slipping when the torque of the couple motor 342 or 344exceeds the point when the tendon 322 or 324 slips on capstan 332 or334. In general, it is desirable to have maximum and minimum tensionsT_(MAX) and T_(MIN) set by both hardware and software. In particular,maximum tension T_(MAX) should be set to avoid damage to the instrumentresulting from large forces, and tension T_(MIN) should be set to ensurethat tendons in the transmission system do not slack and become derailedor tangled.

Step 565 of FIG. 5A generates a control signal that causes actuator 440to apply tension T calculated in step 560. For example, the controlsignal when actuator 440 is a direct drive electrical motor may be adrive current that is controlled to be proportional to calculatedtension T. Control system 450 in step 570 causes actuator 440 to applyand hold the calculated tension T for a time interval Δt, during whichtime, joint 410 moves toward the current desired position θ_(D). Whenchanging the tension T, the application of the full tension T will bedelayed by a time depending on the inertia of actuator 440. Preferably,the inertia of actuator 440 is relatively small for rapid response. Forexample, the inertia of a drive motor acting as actuator 440 wouldpreferably be less than five times the inertia of joint 410. After timeΔt, process 500 branches back to step 510 to repeat measurement of thejoint position, acquisition of the target position and velocity, andcalculation of the tension T to be applied during the next timeinterval. In general, time Δt should be small enough to provide motionthat appears to be smooth to the operator of the instrument and whichdoes not cause undesirable vibrations in the instrument. For example,calculating and setting tension T two hundred and fifty times per secondor more will provide movement that appears smooth to the human eye andwill provide instrument operation that is responsive to human commands,e.g., to human manipulation of controller 460. Use of the errors in thecalculation of the tension T will generally cause joint 410 to convergeon the desired positions with or without the computation of integraltension T_(INT) and without detailed modeling or measurement of theinstrument or the external environment. However, as described above,parameters such as gains g1 and g2 used in calculating the appliedtension T can be tuned for specific instruments and further tuned in useto compensate for changes in the external environment of the instrument.

The tension that actuator 442 applies to transmission system 422 canalso be controlled using control process 500 of FIG. 5A, and parametersuse in process 500 for actuator 442 and transmission system 422 can bethe same or different from those used for actuator 440 and transmissionsystem 420 based on the similarities and differences of actuator 442 andtransmission system 422 when compared to actuator 440 and transmissionsystem 420. In particular, the sign value T_(sign) for actuator 442 inthe configuration of FIG. 4 will be opposite to the sign value T_(sign)for actuator 440 because transmission systems 422 and 420 connect torotate joint 410 in opposite directions. As a result, the primarytension contribution T_(DIST) calculated in step 525 will typically benegative for one actuator 440 or 442. Step 560, which calculates theapplied tension T, can set a negative tension sumT_(DIST)+T_(PROX)+T_(PAIR)+T_(INT) to the minimum tension T_(MIN) asshown in FIG. 5D. Accordingly, parameters, e.g., constant C, for thecalculation of distal tension T_(DIST) in step 525 can generally beselected based on the assumption that the other actuator will apply theminimum tension T_(MIN).

The principles described above for control of a single joint in amedical instrument can also be employed to simultaneously controlmultiple joints in an instrument. FIG. 6 schematically illustrates amulti jointed medical instrument 600 and some quantities used in controlprocesses for instrument 600. Instrument 600 includes L joints 610-1 to610-L, generically referred to herein as joints 610. Each joint 610provides a range of relative positions or orientations of adjacentmechanical members and typically has one or two degrees of freedom ofmotion as described further below. Joints 610 of instrument 600 providea total of N degrees of freedom, where the number N of degrees offreedom is greater than or equal to the number L of joints 610, and theconfigurations of degrees of freedom of joints 610 can be describedusing N-components or a vector θ. An N-component velocity vector {dotover (θ)} is associated with the vector θ. Torques τ₁ to τ_(N), whichmove joints 610-1 to 610-L, respectively correspond to the N componentsof vector θ in that torques τ₁ to τ_(N) tend to cause respectivecomponents of vector θ to change.

Joints 610 are actuated using M transmission systems 620-1 to 620-M(generically referred to herein as transmission systems 620) and Mactuators 640-1 to 640-M (generically referred to herein as actuators640). Transmission systems 620 and actuators 640 can be similar oridentical to transmission systems 420 and actuators 440, which aredescribed above with reference to FIG. 4. In general, the number M oftransmission systems 620 and actuators 640 is greater than the number Nof degrees of freedom, but the relationship between M and N depends onthe specific medical instrument and the mechanics of joints in theinstrument. For example, a joint 610 providing a single degree offreedom of motion may be actuated using two transmission systems 620,and a joint 610 providing two degrees of freedom may be actuated usingthree or four transmission systems 620. Other relationships betweendegrees of freedom and actuating transmission systems are possible.Control system 650 operates actuators 640-1 to 640-M to selectrespective tensions T₁ to T_(M) that actuators 640-1 to 640-Mrespectively apply to transmission systems 620-1 to 620-M.

Control system 650 for instrument 600 can use a distal sensor (notshown) to determine position and velocity vectors θ and {dot over (θ)}associated with joints 610. (Position and velocity are used here toinclude the values and movement of linear or angular coordinates.)Control system 650 also determines desired position and velocity vectorsθ_(D) and {dot over (θ)}_(D) of joints 610. As described further below,the desired position and velocity vectors θ_(D) and {dot over (θ)}_(D)depend on input from a manual controller 660 that may be manipulated bya surgeon using instrument 600. In general, the desired position andvelocity vectors θ_(D) and {dot over (θ)}_(D) will further depend on thecriteria or constraints defined in the control process implemented usingcontrol system 650.

FIG. 7 illustrates a control process 700 in accordance with anembodiment of the invention for controlling a multi jointed instrumentsuch as instrument 600 of FIG. 6. Process 700 begins in step 710 byreading the joint position vector θ from one or more position sensors inthe instrument. The velocity vector {dot over (θ)} can be determinedusing a direct measurement of joint movement or through calculation ofthe change in position measurements between two times. Control system650 receives a surgeon's instructions in step 715. The surgeon'sinstructions can indicate a desired position and velocity of a specificworking portion of the instrument. For example, a surgeon throughmanipulation of manual control 660 can indicate a desired position,velocity, orientation, and rotation of the distal tip or end effector ofthe instrument such as described in U.S. Pat. No. 6,493,608, entitled“Aspects of a Control System of a Minimally Invasive SurgicalApparatus,” which is incorporated herein by reference. Step 720 thenconverts the instructions from manual controller 660 into desiredposition and velocity vectors θ_(D) and {dot over (θ)}_(D) for joints610. For example, given the desired position, orientation, velocity, andangular velocity of the distal tip of instrument 600 of FIG. 6, controlsystem 650 can calculate desired joint position and velocity vectorsθ_(D) and {dot over (θ)}_(D) that will achieve the desired tipconfiguration. The conversion step 720 can be achieved with well-knowntechniques, such as differential kinematics inversion as described by“Modeling and Control of Robot Manipulators,” L. Sciavicco and B.Siciliano, Springer, 2000, pp. 104-106 and “Springer Handbook ofRobotics,” Bruno Siciliano & Oussama Khatib, Editors, Springer, 2008,pp. 27-29, which are incorporated herein by reference. Above-referencedU.S. Pat. No. 6,493,608, entitled “Aspects of a Control System of aMinimally Invasive Surgical Apparatus,” also describes techniques fordetermining desired joint position and velocity vectors θ_(D) and {dotover (θ)}_(D) that will achieve the desired tip configuration. It shouldbe noted that for instruments with a kinematic redundancy, i.e., if thenumber of degrees of freedom of motion provided by joints 610 is largerthan the number of degrees of freedom of the motion command specified bymanual controller 660, the redundancy can be resolved with standardtechniques such as those described in Yoshihiko Nakamura, “AdvancedRobotics: Redundancy and Optimization,” Addison-Wesley (1991).

It should also be appreciated that software enforced constraints betweenthe joints of the instruments can also be enforced when solving theinverse kinematics problem on the desired command for the instrument.For instance, the joint positions and velocity commands of two jointscan be forced to be the same or opposite or in a given ratio,effectively implementing a virtual cam mechanism between the joints.

Step 725 computes a position error vector (θ_(D)−θ) and velocity errorvector ({dot over (θ)}_(D)−{dot over (θ)}), and step 730 uses componentsof error vectors (θ_(D)−θ) and ({dot over (θ)}_(D)−{dot over (θ)}) forcalculation of respective torque components τ₁ to τ_(N). In one specificembodiment, each torque component τ_(i) for an index i from 1 to N isdetermined using Equation 2. In Equation 2, g1 _(i) and g2 _(i) are gainfactors, and C_(i) is a constant or geometry-dependent parameter thatmay be selected according to known or modeled forces applied to thejoint by other portions of the system. However, parameter C_(i) is notrequired to strictly be a constant but could include non-constant termsthat compensate for properties such as gravity or mechanism stiffnessthat can be effectively modeled, and accordingly, C_(i) may depend onthe measured position or velocity of the joint 610-i on which the torqueτ_(i) acts. In general, gain factors g1 _(i) and g2 _(i) and constantC_(i) can be selected according to the desired stiffness and dampeningor responsiveness of a joint or according to an accumulation of error.For example, when inserting the instrument 600 to follow a natural lumenwithin a patient, the gain factor g1 _(i) can be set to a low value tomake a joint behave gently and prevent the joint action from harmingsurrounding tissue. After the insertion, the gain factor g1 _(i) can beset to a higher value that allows the surgeon to perform a precisesurgical task with the instrument. Other equations or corrections toEquation 2 could be employed in the determination of the torque. Forexample, the calculated torque could include a correction proportionalto a saturated integral of the difference between the currentmeasurement of joint position and the desired joint position that thepreviously applied torque was intended to achieve. Such correction usinga saturated integral could be determined as described above for thesingle joint control process of FIG. 5A and particularly illustrated bysteps 530 and 535 of FIG. 5A.

τ_(i) =g1_(i)(θ_(D)−θ)_(i) +g2_(i)({dot over (θ)}_(D)−{dot over(θ)})_(i) +C _(i)  Equation 2

Step 735 uses the torques computed in step 730 to determine distaltensions T_(DIST). Distal tension T_(DIST) is an M component vectorcorresponding to transmission systems 620-1 to 620-M and actuators 640-1to 640-M. The determination of the distal tensions depends on geometryor mechanics between the instrument joints and transmission systems. Inparticular, with multiple joints, each joint may be affected not only bythe forces applied directly by transmission systems attached to thejoint but also by transmission systems that connect to joints closer tothe distal end of the instrument. The torques and tensions in a medicalinstrument can generally be modeled using equations of the form ofEquation 3. In Equation 3, τ₁ to τ_(N) are components of the torquevector, and T₁ to T_(M) are the distal tensions respectively in Mtransmission systems 620 that articulate joints 610. Each coefficienta_(IJ) for index I=1 to N and index J=1 to M generally corresponds tothe effective moment arm of the tension T_(J) for joint and rotationaxis corresponding to torque τ_(I).

$\begin{matrix}{\begin{bmatrix}\tau_{1} \\\tau_{2} \\\vdots \\\tau_{N}\end{bmatrix} = {{\begin{bmatrix}a_{11} & a_{12} & \ldots & a_{1\; M} \\a_{21} & a_{22} & \ldots & a_{2\; M} \\\vdots & \vdots & \ddots & \vdots \\a_{N\; 1} & a_{N\; 2} & \ldots & a_{NM}\end{bmatrix}\begin{bmatrix}T_{1} \\T_{2} \\\vdots \\T_{M}\end{bmatrix}} = {A\begin{bmatrix}T_{1} \\T_{2} \\\vdots \\T_{M}\end{bmatrix}}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

The computation in step 735 thus corresponds to solving N equations forM variables T₁ to T_(M). Since M is generally greater than N, thesolution is not unique, so that inequality constraints can be selected,such as the constraint that all tensions are greater than a set ofminimum values, and optimality conditions, such as the condition that aset of tensions of lowest maximum value is chosen, can be applied toprovide a unique solution with desired characteristics such as minimaltensions that stay above a desired threshold in all or selected joints.The matrix inversion problem of Equation 3 with inequality andoptimality constraints such as minimal tension constraints can be solvedby some well-known techniques such as the SIMPLEX method of linearprogramming. (See, for example, “Linear Programming 1: Introduction,”George B. Dantzig and Mukund N. Thapa, Springer-Verlag, 1997, which isincorporated herein by reference in its entirety.) In accordance with afurther aspect of the invention, the distal tensions can be determinedusing a process that sequentially evaluates joints beginning with themost distal joint and solves for tensions in transmission systems thatconnect to each joint based on geometric parameters and the tensionspreviously calculated for more distal joints.

Control system 650 in one embodiment of process 700 activates actuators640 to apply the distal tensions calculated in step 735 to respectivetransmission systems 620. Alternatively, corrections to the distaltensions can be determined as illustrated by steps 740 and 745. Inparticular, step 740 computes a correction tension T_(PROX), whichdepends on the difference between a desired transmission velocity vector{dot over (θ)}_(DL), computed based on desired joint velocity {dot over(θ)}_(D), and a current transmission velocity vector {dot over (θ)}_(L),computed based on the current actuator velocity {dot over (θ)}_(A). Inone particular embodiment, the desired transmission velocity can be themultiplication of the transpose of the coupling matrix A in Equation 3with the desired joint velocity {dot over (θ)}_(D), while the currenttransmission velocity can be the product of the actuator velocity {dotover (θ)}_(A) and respective moment arm of actuators 640. Correctiontension T_(PROX) can compensate for inertia or other effects between theactuator 640 and the connected joint 610 and, in one embodiment, is afunction of the difference ({dot over (θ)}_(DL)−{dot over (θ)}_(L)) suchas the product of difference ({dot over (θ)}_(DL)−{dot over (θ)}_(L))and a gain factor. Step 745 computes a correction tension T_(PAIR),which depends upon a difference or differences between the velocities ofactuators that actuate the same joint. For example, in the case in whicha joint provides one degree of freedom of motion and is actuated by apair of actuators connected to the joint through a pair of transmissionsystems, correction tension T_(PAIR) can be determined as a function ofthe difference between the velocities of the two actuators. (See, forexample, step 550 of FIG. 5A as described above.) Corrections similar tocorrection tension T_(PAIR) can be generalized to the case where threeor more transmission systems and actuators actuate a joint having twodegrees of freedom of motion.

Step 750 combines distal tension T_(DIST) and any corrections T_(PROX)or T_(PAIR) to determine a combined tension T applied by the actuators.In general, each component T₁ to T_(M) of the combined tension T can belimited to saturate at a maximum tension T_(MAX) or a minimum tensionT_(MIN) if the sum of the calculated distal tensions T_(DIST) andcorrections T_(PROX) and T_(PAIR) is greater than or less than thedesired maximum or minimum values as described above with reference toFIG. 5D. Steps 755 and 760 then activate actuators 640 to apply and holdthe combined tension T for a time interval Δt before process 700 returnsto step 710 and reads the new joint positions. Holding the tension foran interval of roughly 4 ms or less, which corresponds to a rate of 250Hz or higher, can provide smooth movement of an instrument for a medicalprocedure.

Medical instruments commonly require that the working tip or endeffector of the instrument have a position and orientation that anoperator such as a surgeon can control. On the other hand, the specificposition and orientation of each joint is generally not critical to theprocedure being performed, except where joint position or orientation ismandated by the lumen through which the instrument extends. Inaccordance with an aspect of the invention, one approach to control amulti joint instrument selects tensions applied through tendons usingdifferences between current and desired configurations of the tip of aninstrument. For example, differences between the measured position,orientation, velocity, and angular velocity of the tip of the instrumentand the desired position, orientation, velocity, and angular velocity ofthe tip of the instrument can control the tensions applied to tendons ofa medical instrument.

FIG. 7B illustrates a control process 700B in accordance with anembodiment of the invention. Process 700B employs some of the same stepsas process 700, and those steps have the same reference numbers in FIGS.7A and 7B. Process 700B in step 710 reads or determines the jointpositions θ and joint velocities {dot over (θ)} from a sensor or sensorsin the medical instrument and in step 712 reads or determines aposition, orientation, velocity, and angular velocity of a tip of theinstrument. Tip here refers to a specific mechanical structure in theinstrument and may be an end effector such as forceps, scissors, ascalpel, or a cauterizing device on the distal end of the instrument. Ingeneral, the tip has six degrees of freedom of motion and has aconfiguration that can be defined by six component values, e.g., threeCartesian coordinates of a specific point on the tip and three anglesindicating the pitch, roll, and yaw of the tip. Velocities associatedwith changes in the configuration coordinates over time may be directlymeasured or calculated using measurements at different times. Givenjoint positions and velocities θ and {dot over (θ)} and a prioriknowledge of the kinematic model of the instrument 610, one can buildboth forward and differential kinematic models that allow computing theCartesian position, orientation, translational velocity, and angularvelocity of the tip with respect to the frame of reference of theinstrument 610. The forward and differential kinematic model of akinematic chain can be easily constructed according to known methods.For instance, the procedure described by John J. Craig, “Introduction toRobotics: Mechanics and Control,” Pearson Education Ltd. (2004), whichis incorporated herein by reference, may be used. Step 715 determinesthe desired tip position, orientation, translational velocity, andangular velocity, which can be performed in the manner described above.

In another embodiment, a sensor, for example, a shape sensor, may beused to directly measure Cartesian position and orientation as describedin U.S. Pat. App. Pub. No. 20090324161 entitled “Fiber optic shapesensor” by Giuseppe M. Prisco, which is incorporated herein byreference. Translational velocities associated with changes in theconfiguration coordinates over time may be calculated using measurementsat different times. Unlike the translational velocities, the angularvelocities cannot be computed simply by the differencing approach due tothe angular nature of the quantities. However, the methods of computingthe angular velocities associated with the changes in orientation areknown in the art and described, for example, by L. Sciavicco and B.Siciliano, “Modelling and Control of Robot Manipulators,” Springer 2000,pp. 109-111.

Process 700B in step 722 calculates tip errors. In one embodiment, step722 includes calculating a position error or difference e_(POS) betweenthe desired Cartesian coordinates of the tip and the current Cartesiancoordinates of the tip, a translational velocity error or differencee_(VT) between the desired translational velocity of the tip and thecurrent translational velocity of the tip, an orientation error ordifference e_(ORI) between the desired orientation coordinates of thetip and the current orientation coordinates of the tip, and an angularvelocity error or difference e_(VA) between the desired angular velocityof the tip and the current angular velocity of the tip. Unlike theposition error e_(POS), the orientation error e_(ORI) cannot be computedsimply by the differencing approach due to the angular nature of thequantities. However, the methods of computing the change in orientationare known in the art and can be found in robotics literatures, forexample, L. Sciavicco and B. Siciliano, “Modelling and Control of RobotManipulators,” Springer, 2000, pp. 109-111.

In step 724, process 700B determines a tip force F_(TIP) and a tiptorque τ_(TIP) that are intended to move tip from the currentconfiguration to the desired configuration. In this embodiment of theinvention, tip force F_(TIP) depends on errors e_(POS) and e_(VT). Forexample, each component F_(X), F_(Y), or F_(Z) of tip force F_(TIP) canbe calculated using Equation 4, where gp_(i) and gv_(i) are gain factorsand Cf_(i) is a constant. The tip torque τ_(TIP) can be determined in asimilar manner, in which each component of tip torque τ_(i) is afunction of errors e_(ORI) and e_(VA) with another set of gain factorsand constants gori_(i), gva_(i), and Cτ_(i) as shown in Equation 5. Ingeneral, the gain factors gp_(i) and gv_(i) associated with differentforce or torque components F_(i) and τ_(i) can be different. Havingseparate gain factors and constants for each component of tip forceF_(TIP) and tip torque τ_(i) provides flexibility in specifying thedynamic behavior of the end effector or instrument tip, enhancing moreeffective instrument interaction with the tissue. For instance, whennavigating the instrument into a small lumen, one may set low values forthe gain factors of tip force perpendicular to the inserting directionwhile have high values for the gain factors along the insertingdirection. With that, the instrument is sufficient stiff for insertionwhile having low lateral resistance to the tissue, preventing damage tothe surrounding tissue. Another example, when using the instrument topunch a hole in the tissue in certain direction, having high values inthe gain factors of the tip torque as well as the gain factor along theinserting direction of the tip force, facilitate the hole-punch task.

F _(i) =gp _(i) *e _(POS) +gv _(i) *e _(VT) +Cf _(i)  Equation 4

τ_(i) =gori _(i) *e _(ORI) +gva _(i) *e _(VA) +Cτ _(i)  Equation 5

Step 732 determines a set of joint torques that will provide the tipforce F_(TIP) and tip torque τ_(TIP) determined in step 724. Therelationships between joint torque vector τ, tip force F_(TIP), and tiptorque τ_(TIP) are well-documented and normally described as in Equation6, where J^(T) is the transpose of the well-known Jacobian Matrix J of akinematic chain of the instrument.

$\begin{matrix}{\tau = {J^{T}\begin{bmatrix}F_{TIP} \\\tau_{TIP}\end{bmatrix}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

The Jacobian Matrix J depends on the geometry of the instrument and thecurrent joint positions determined in step 710 and can be constructedusing known methods. For example, John J. Craig, “Introduction toRobotics: Mechanics and Control,” Pearson Education Ltd. (2004), whichis incorporated herein by reference, describes techniques that may beused to construct the Jacobian Matrix for a robotic mechanism. In somecases, if there are extra or redundant degrees of freedom of motionprovided in the medical instrument, e.g., more than the six degrees offreedom of motion of the tip, the set of joint torques that provides tipforce F_(TIP) and tip torque T_(TIP) is not unique, and constraints canbe used to select a set of joint torques having desired properties,e.g., to select a set of joint torques that prevents the joints reachingtheir mechanical joint limits in range of motion or supported loads orto enforce extra utility on any particular joints of the instrumentduring manipulation. For instance, one can prevent the joints reachingtheir mechanical joint limits by selecting a set of joint torques thatminimizes the deviation from the midrange joint positions, from the nullspace associated with the transpose of Jacobian matrix J^(T). The set ofjoint torques can be selected according to Equation 7. In Equation 7,P(θ) is a potential function that define addition utility to be providedby the solution, ∇ is a gradient operator, N( ) is a null spaceprojection operator that selects a set of joint torques from the nullspace of the transpose of Jacobian matrix J^(T), associated with itsinput. In one embodiment, potential P(θ) a quadratic function of thejoint positions that has a minimum when the joints are in the center oftheir range of motion. The gradient of the potential function −∇P(θ)selects a set of joint torques that draws joints moving toward thecenter of their range of motion while the null space projection operatorN( ) enforces that the selected set of joint torques providing thedesired tip force and tip torques also satisfy the additional utility.Techniques for using constraints in robotic systems providing redundantdegrees of freedom of motion are known in the art and can be found inrobotics literatures. See, for instance, Yoshihiko Nakamura, “AdvancedRobotics: Redundancy and Optimization,” Addison-Wesley (1991) andliterature by Oussama Khatib, “The Operational Space Framework,” JSMEInternational Journal, Vol. 36, No. 3, 1993.

$\begin{matrix}{\tau = {{J^{T}\begin{bmatrix}F_{TIP} \\\tau_{TIP}\end{bmatrix}} + {N\left( {- {\nabla\; {P(\theta)}}} \right)}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Process 700B after step 732 proceeds in the same manner as process 700described above. In particular, based on the joint torques determined instep 732, step 735 determines tensions T_(DIST). Steps 740 and 745determine corrections T_(PROX) and T_(PAIR) to tensions T_(DIST), andstep 750 determines a combined tension vector T. Steps 755 and 760 thenapply and hold the components of combined tension vector T on thetransmission systems to actuate the medical instrument during a timeinterval Δt.

Processes 700 and 700B of FIGS. 7A and 7B required determination oftensions that will produce a particular set of joint torques. The tendontension for a single isolated joint can be determined from a jointtorque simply by dividing the joint torque by the moment arm at whichthe tension is applied. In the multi joint case, due to geometry of thetransmission system and cable routing and redundancy in the actuationcable, the problem amounts to solving a system of equations withconstraints. In one particular embodiment, one may apply non-negativetendon tension constraints (or minimum tension constraints) when solvingthe system of equations to prevent slacking in the cables or othertendons in the transmission systems. The inputs of the problem are thedetermined joint torque for each joint while the geometry of cablerouting defines the system of equations (or the coupling matrix A ofEquation 3). Appropriate tendon tensions are needed that fulfillEquation 3 and are larger than minimum tension constraints. A standardoptimization method, called SIMPLEX method can be used to handle thismatrix inverse problem with inequality and optimality constraints. TheSIMPLEX method requires a relatively larger computation time and may notbe advantageous to be used in real time application. Also, the SIMPLEXmethod does not guarantee continuity in the solutions as the jointtorques change. To speed-up the computation efficiency and provide acontinuous output solution, an iterative approach can be consideredwhich relies on the triangular nature of the coupling matrix A. FIGS.8A, 8B, 8C, 9A, 9B, 9C, 9D, and 9E illustrate a few specific examples ofjoints in multi jointed instruments and are used herein to illustratesome properties of the coupling matrix A in Equation 3.

FIG. 8A, for example, illustrates a portion of an instrument thatincludes multiple mechanical joints 810, 820, and 830. Each joint 810,820, or 830 provides a single degree of freedom, which corresponds torotation about an axis z1, z2, or z3 of the joint. In FIG. 8A, tendonsC1 and C2 connect to joint 810 for actuation of joint 810. Tendons C3and C4 pass through joint 810 and connect to joint 820 for actuation ofjoint 820. Tendons C5 and C6 pass through joints 810 and 820 and connectto join 830 for actuation of joint 830. The proximal ends (not shown) oftendons C1 to C6 can be connected though compliant transmission systemssuch as illustrated in FIG. 2 or 3A to respective drive motors or otheractuators. The control system for the instrument controls the actuatorsto apply respective tensions T1, T2, T3, T4, T5, and T6 in tendons C1,C2, C3, C4, C5, and C6.

Joint 830 is at the distal end of the instrument in the illustratedembodiment, and actuation of joint 830 could be controlled using asingle-joint process such as described above with reference to FIGS. 5A,5B, 5C, and 5D. However, the total torque on joint 820 depends not onlyon the tensions in cables C3 and C4 but also the torque applied bytendons C5 and C6, which are connected to joint 830. The total torque onjoint 810 similarly depends not only on the tensions in tendons C1 andC2 but also the torque applied by tendons C3, C4, C5, and C6, which areconnected to joints 820 and 830 that are closer to the distal end.Models based on the geometric or kinematic characteristics of theinstrument can be developed to relate the torques τ1, τ2, and τ3 onjoints 810, 820, and 830 to the tension in tendons T1, T2, T3, T4, T5,and T6. Equation 3A illustrates one such mathematical model and providesa specific example of Equation 3 above. In Equation 3A, τ₁, τ₂, and τ₃are the respective actuating torques on joints 810, 820, and 830, r₁,r₂, and r₃ are the effective moment arms at which tendons C1, C3, and C5attach, and T1, T2, T3, T4, T5, and T6 are the tensions in respectivetendons C1, C2, C3, C4, C5, and C6. The model that leads to Equation 3Aapplies to a specific set of geometric or mechanical characteristics ofthe instrument including joints 810, 820, and 830 including that:rotation axes z1, z2, and z3 are parallel and lie in the same plane;tendons C1 and C2, C3 and C4, or C5 and C6 respectively attach ateffective moment arm r1, r2, or r3; and tendons C1, C3, and C5 operateon respective joints 810, 820, and 830 in rotation directions oppositefrom the operation of tendons C2, C4, and C6, respectively.

$\begin{matrix}{\begin{bmatrix}\tau_{1} \\\tau_{2} \\\tau_{3}\end{bmatrix} = {\begin{bmatrix}r_{1} & {- r_{1}} & r_{2} & {- r_{2}} & r_{3} & {- r_{3}} \\0 & 0 & r_{2} & {- r_{2}} & r_{3} & {- r_{3}} \\0 & 0 & 0 & 0 & r_{3} & {- r_{3}}\end{bmatrix} \cdot \begin{bmatrix}{T\; 1} \\{T\; 2} \\{T\; 3} \\{T\; 4} \\{T\; 5} \\{T\; 6}\end{bmatrix}}} & {{Equation}\mspace{14mu} 3A}\end{matrix}$

FIGS. 8B and 8C illustrate characteristics of a medical instrumentincluding joints 810 and 820 with respective rotation axes z1 and z2that are perpendicular to each other. In general, the net torque at eachjoint 810 and 820 depends on the tensions in the tendons passing throughthe joint to the distal end and the effective moment arms associatedwith the tendons relative to the actuation axis of the joint. FIG. 8Cshows a view of a base of joint 810 to illustrate a typical example inwhich each tendon C1, C2, C3, and C4 operates at different moment armsabout axes z1 and z2. Considering joints 810 and 820 as an isolatedsystem or the last two actuated joints on the distal end of aninstrument, the net torques τ₁ and τ₂ on joints 810 and 820 are relatedto the tensions T1, T2, T3, and T4 in respective tendons C1, C2, C3, andC4 as indicated in Equation 3B. In particular, joint 820 is subject to anet torque τ₂ that depends on tension T3 in tendon C3 and a moment arma32 relative to axis z2 at which tendon C3 attaches to joint 820 and thetension T4 in tendon C4 and a moment arm a42 relative to axis z2 atwhich tendon C4 attaches to joint 820. Torque τ₁ on joint 810 depends onthe tensions T1 and T2 in the tendons C1 and C2 attached to joint 810,the tensions T3 and T4 in the tendons C3 and C4 attached to joint 820,and the moment arms a11, a21, a31, and a41. Moment arms a21 and a41 areassigned with a negative sign because pulling tendons C2 and C4 createsthe rotation in a direction opposite from the convention-definedpositive direction for torque τ₁ on joint 810. For the same reason,moment arm a31 is also assigned with a negative sign as pulling tendonC3 causes rotation opposite to the direction of positive rotation ofjoint 820.

$\begin{matrix}{\begin{bmatrix}\tau_{1} \\\tau_{2}\end{bmatrix} = {\begin{bmatrix}{a\; 11} & {{- a}\; 21} & {a\; 31} & {{- a}\; 41} \\0 & 0 & {{- a}\; 32} & {a\; 42}\end{bmatrix}\begin{bmatrix}{T\; 1} \\{T\; 2} \\{T\; 3} \\{T\; 4}\end{bmatrix}}} & {{Equation}\mspace{14mu} 3B}\end{matrix}$

It should be appreciated that a similar method to compute the matrix Ain Equations 3 can be employed when the joint axes are neither parallelor perpendicular to each other but rather at an arbitrary relativeorientation, by computing accordingly the moment arms of each tendonwith respect to each joint axis.

FIG. 9A shows a portion 900 of an instrument including a continuousflexible joint 910 such as is commonly found in medical catheters,endoscopes for the gastrointestinal tract, the colon and the bronchia,guide wires, and some other endoscopic instruments such as graspers andneedles used for tissue sampling. Joint 910 is similar to the flexiblestructure described above with reference to FIG. 3B. However, joint 910is manipulated through the use of three or more tendons 920 to provide ajoint with two degrees of freedom of motion. For example, FIG. 9B showsa base view of an embodiment in which four tendons 920, which arelabeled c1, c2, c3, and c4 in FIG. 9B, connect to an end of flexiblejoint 910. A difference in the tensions in tendons c1 and c2 can turnjoint 910 in a first direction, e.g., cause rotation about an X axis,and a difference in the tensions in tendons c3 and c4 can turn joint 910in a second direction that is orthogonal to the first direction, e.g.,cause rotation about a Y axis. The components τ_(X) and τ_(Y) of the nettorque tending to bend joint 910 can be determined from tensions T1, T2,T3, and T4 respectively in tendons c1, c2, c3, and c4 as indicated inEquation 3C. As can be seen from Equation 3C, equations for torquecomponents τ_(X) and τ_(Y) are not coupled in that component τ_(X)depends only on tensions T1 and T2 and component τ_(Y) depends only ontensions T3 and T4.

$\begin{matrix}{\begin{bmatrix}\tau_{X} \\\tau_{Y}\end{bmatrix} = {\begin{bmatrix}{rx} & {- {rx}} & 0 & 0 \\0 & 0 & {ry} & {- {ry}}\end{bmatrix}\begin{bmatrix}{T\; 1} \\{T\; 2} \\{T\; 3} \\{T\; 4}\end{bmatrix}}} & {{Equation}\mspace{14mu} 3C}\end{matrix}$

FIG. 9C illustrates a base view of an embodiment that uses three tendons920, which are labeled c1, c2, and c3 in FIG. 9C, to actuate joint 910.With this configuration, the components τ_(X) and τ_(Y) of the nettorque tending to bend joint 910 can be determined from tensions T1, T2,and T3 respectively in tendons c1, c2, and c3 as indicated in Equation3D where ra is the moment arm of tendon c1 about the X axis, −rb is themoment arm of tendons c2 and c3 about the X axis, and rc and −rc are therespective moment arms of tendons c2 and c3 about the Y axis. Momentarms of tendons c2 and c3 about X-axis are assigned with a negative signby convention because pulling tendons c2 and c3 will bend joint 910 in adirection opposite from the direction that pulling tendon c1 bends joint910 about the X axis. For the same reason, the moment arm of tendon c3about Y-axis is assigned a negative sign by convention.

$\begin{matrix}{\begin{bmatrix}\tau_{X} \\\tau_{Y}\end{bmatrix} = {\begin{bmatrix}{ra} & {- {rb}} & {- {rb}} \\0 & {rc} & {- {rc}}\end{bmatrix}\begin{bmatrix}{T\; 1} \\{T\; 2} \\{T\; 3}\end{bmatrix}}} & {{Equation}\mspace{14mu} 3D}\end{matrix}$

FIG. 9D illustrates an embodiment in which a flexible instrument 950,e.g., a flexible catheter, contains two joints. A joint 910 is actuatedthrough tendons 920 to provide two degrees of freedom of motion, and ajoint 940 is actuated through tendons 930 to provide another two degreesof freedom of motion. FIG. 9E illustrates the base of joint 940 in aspecific case that uses three tendons 920 (labeled c1, c2, and c3 inFIG. 9E) for joint 910 and three tendons 930 (labeled c4, c5, and c6 inFIG. 9E) for joint 940. The relationships between torques and forces inthe most distal joint 910 may be modeled using Equation 3D above.However, the torques in joint 940 depend on the tensions in all of thetendons 920 and 930 that pass through flexible section 940. The torquesand tensions in instrument 950 may thus be related in one specificexample as indicated in Equation 3E. In Equation 3E, τ1 _(X) and τ1 _(Y)are torque components in joint 910, τ2 _(X) and τ2 _(Y) are torquecomponents in joint 940, ra, rb, and rc are the magnitudes of momentarms, T1, T2, and T3 are tensions in tendons 920, and T4, T5, and T6 aretensions in tendons 930.

$\begin{matrix}{\begin{bmatrix}{\tau \; 2_{X}} \\{\tau \; 2_{Y}} \\{\tau \; 1_{X}} \\{\tau \; 1_{Y}}\end{bmatrix} = {\begin{bmatrix}{- {ra}} & {rb} & {rb} & {ra} & {- {rb}} & {- {rb}} \\0 & {- {rc}} & {rc} & 0 & {rc} & {- {rc}} \\0 & 0 & 0 & {ra} & {- {rb}} & {- {rb}} \\0 & 0 & 0 & 0 & {rc} & {- {rc}}\end{bmatrix}\begin{bmatrix}{T\; 1} \\{T\; 2} \\{T\; 3} \\{T\; 4} \\{T\; 5} \\{T\; 6}\end{bmatrix}}} & {{Equation}\mspace{14mu} 3E}\end{matrix}$

Equations 3A to 3E illustrate that in many medical instruments theproblem of finding tensions that provide a particular torque in the mostdistal joint can be solved independently of the other tensions in thesystem. More generally, the joint torque for each joint depends on thetensions in the tendons that connect to that joint and on the tensionsapplied to more distal joints. Step 735 of processes 700 and 700B ofFIGS. 7A and 7B can thus be performed using a process that iterativelyanalyzes joints in a sequence from the distal end of the instrumenttoward the proximal end of the instrument to determine a set of tensionsthat produces a given set of joint torques.

FIG. 10 shows an iterative process 735 for computing tensions thatproduce a given set of joint torques. Process 735 in the embodiment ofFIG. 10 starts with a tension determination for the last or most distaljoint and then sequentially determines tensions for joints in an ordertoward the first or most proximal joint. Step 1010 initializes an indexj, which identifies a joint for analysis and is initially set to thenumber L of joints. Step 1020 then acquires the torque τ_(j) for the jthjoint. The joint torque T_(j) may, for example, be determined as in step730 of process 700 or step 732 of 700B as described above and may have asingle non-zero component for a joint providing a single degree offreedom of motion or two non-zero components for a joint providing twodegrees of freedom of motion.

Step 1030 then calculates the tensions to be directly applied to the jthjoint through the linkages attached to the jth joint in order to producethe net torque, e.g., computed in step 730 or 732 of FIG. 7A or 7B. Inthe example of FIG. 10, computation of step 1030 is under the constraintthat one of the directly applied tensions is a target or nominaltension. The nominal tension may be but is not required to be zero sothat tension in the transmission system is released or alternatively theminimum tension that ensures that the tendons in the transmissionsystems do not become slack. The nominal tension may but is not requiredto correspond to a case in which actuator force is released, e.g., wheredrive motors 640 of FIG. 6 are freewheeling, in which case the tensionmay depend on type of transmission system employed.

In the specific case in which jth joint in the medical instrumentprovides a single degree of freedom of motion and is directly coupled totwo tendons or transmission systems, the joint torque has a singlecomponent that is related to the tensions by a single equation fromamong Equations 3. Step 1030 for the Lth or most distal joint theninvolves solving a linear equation relating the joint torque to the twotensions coupled to the most distal joint. With a single linear equationinvolving two unknown tensions, applying the constraint that one tensionis the nominal tension guarantees a unique solution for the othertension. In particular, the other tension can be uniquely determinedfrom the torque on the most distal joint and the relevant coefficientsof the coupling matrix A. Alternatively, if the Lth joint provides twodegrees of freedom of motion and is coupled to three tendons ortransmission systems, the joint torque has two components andcorresponds to two equations from among Equations 3. The two equationsinvolve three tensions, so that with the constraint that one of thetensions be equal to the nominal tension, the other two tensions can beuniquely determined from the components of the joint torque and therelevant components of the coupling matrix A. It should be noted thatthe proposed method is general in the sense that, in a similar fashion,if m tendons, with m greater than three, are connected to the same jointthat provides two degrees of freedom, then (m−2) tensions can beconstrained at the same time to be equal to the nominal tension, whilethe remaining two tensions will be uniquely determined from thecomponents of the joint torque and the relevant components of thecoupling matrix A.

Step 1030 is initially executed for the most distal joint (i.e., j=L).Substep 1032 of step 1030 initially selects one of the transmissionsystems attached to the most distal joint, and substep 1034 sets thattension to the nominal tension for a trial calculation in substep 1036.Substep 1036 initially calculates tension (or tensions) for the othertransmission systems attached to the joint, and the calculated tensionsonly depend on the computed joint torque and the other tensions directlyapplied to the most distal joint. Step 1038 determines whether all ofthe calculated tensions are greater than or equal to the minimumpermitted tension. If not, step 1040 selects another of the transmissionsystems directly coupled to the joint to be the transmission system withthe nominal tension when steps 1034 and 1036 are repeated. Once step1040 determines that the calculated tension or tensions are all greaterthan or equal to the minimum allowed tension, the determination of thetension for the most distal joint is complete, and step 1050 decrementsthe joint index j before process 735 branches back from step 1060 forrepetition of step 1020.

Step 1030 for the jth joint in the case of a joint connected to twotransmission systems and providing one degree of freedom of motioninvolves evaluation of a single equation from among Equations 3. Asdescribed above, the nature of the coupling matrix A is such that theequation for the jth joint involves only the tensions directly coupledto the Jth joint and the tensions coupled to more distal joints.Accordingly, if the tensions for more distal joints have already beendetermined, the equation associated with the jth joint involves only twounknowns, which are the tensions in the transmission systems directlyconnected to the joint. The constraint that one of the tensions be thenominal tension allows unique determination of the other tension that islarger than or equal to the nominal tension. The case where the jthjoint connects to three transmission systems and provides two degrees offreedom of motion involves evaluation of the two equations associatedwith the two components of the joint torque. If the tensions for moredistal joints have already been determined, the equations associatedwith the jth joint involves only three unknowns, which are the tensionsin the tendons directly connected to the joint. The constraint that oneof the tensions be the nominal tension allows unique determination ofthe other two tensions that are larger than or equal to the nominaltension.

Process 735 of FIG. 10 can thus use tension determinations in the orderof the joints from the distal end of the instrument to generate acomplete set of distal tensions that is output in step 1070 when step1060 determines that the most proximal joint has been evaluated. Process735 can be efficiently implemented using a computer or other computingsystem operating for real time determination of tensions that arechanged at a rate that provides motion smooth enough for medicalprocedures, e.g., at rates of up to 250 Hz or more. Further, theconstraint that each joint have at least one directly applied tension ata target or nominal value provides continuity between the tensionsdetermined at successive times.

The processes described above can be implemented or controlled usingsoftware that may be stored on computer readable media such aselectronic memory or magnetic or optical disks for execution by ageneral purpose computer. Alternatively, control of or calculationsemployed in the above-described processes can be implanted usingapplication-specific hardware or electronics.

Although the invention has been described with reference to particularembodiments, the description is only an example of the invention'sapplication and should not be taken as a limitation. Various adaptationsand combinations of features of the embodiments disclosed are within thescope of the invention as defined by the following claims.

1. A medical instrument system including: a plurality of joints; aplurality of actuators; a plurality of transmission systems havingproximal ends respectively coupled to the actuators, each of thetransmission systems having a distal end attached to an associated oneof the joints to allow the transmission of a force for articulation ofthe medical instrument system; a sensor coupled to measure configurationof the medical instrument; and a control system coupled to receiveconfiguration measurements, wherein the control system uses theconfiguration measurements to determine tensions for the transmissionsystems and operates the actuators to produce the tensions in thetransmission systems.
 2. The system of claim 1, wherein each of thetransmission systems is compliant and stretches under a regulated valueof the actuator force by an amount corresponding to more than apermitted inaccuracy in joint articulation.
 3. The system of claim 1,wherein the control system regulates the tensions applied to thetransmission systems to be independent of positions of the actuators. 4.The system of claim 1, wherein the control system regulates the tensionsapplied to the transmission systems to be independent of the complianceof the transmission systems or the joints.
 5. The system of claim 1,wherein the control system regulates the tensions applied to thetransmission systems to be independent of the length of the transmissionsystems from their proximal ends to their distal ends.
 6. The system ofclaim 1, wherein the control system regulates the tensions applied tothe transmission systems to be independent of shape of the transmissionsystems from their proximal ends to their distal ends.
 7. The system ofclaim 1, wherein the control system determines the tensions using aprocess comprising: determining differences between a desiredconfiguration of the joints and a current configuration of the joints;determining from the differences, joint torques that actuate the jointsto reduce the differences; and determining the tensions that produce thejoint torques.
 8. The system of claim 1, wherein the control system usesthe configuration measurements in a process including: determining afirst difference between a current configuration of a selected one ofthe joints and a desired configuration of the selected joint; and usinga first product of the first difference and a first gain factor indetermining a joint torque that actuates the selected joint.
 9. Thesystem of claim 8, wherein the process in which the control system usesthe configuration measurements further comprises: determining a seconddifference between a current velocity at the selected joint and adesired velocity at the joint; and determining a second product of thesecond difference and a second gain factor, wherein the joint torquethat actuates the selected joint further depends on the second product.10. The system of claim 1, wherein the control system determines thetensions using a process comprising: determining differences between adesired configuration of a tip of the instrument and a currentconfiguration of the tip; determining from the differences, a tip forceand a tip torque that when applied to the tip reduces the differences;determining joint torques that produce the tip force and the tip torqueon the tip of the instrument; and determining the tensions that producethe joint torques.
 11. The system of claim 10, wherein determining thetip force comprises: determining a first difference between a currentvalue of a first position coordinate of the tip and a desired value ofthe first position coordinate of the tip; determining a first product ofthe first difference and a first gain factor; and using the firstproduct in determining a first component of the tip force.
 12. Thesystem of claim 11, wherein determining tip force further comprises:determining a second difference between a current value of a secondposition coordinate of the tip and a desired value of the secondposition coordinate of the tip; determining a second product of thesecond difference and a second gain factor, wherein the second gainfactor is different from the first gain; and using the second product indetermining a second component of the tip force.
 13. The system of claim10, wherein determining the tip torque comprises: determining a firstdifference between a current value of a first angular coordinate of thetip and a desired value of the first angular coordinates of the tip;determining a first product of the first difference and a first gainfactor; and using the first product in determining a first component ofthe tip torque.
 14. The system of claim 13, wherein determining the tiptorque further comprises: determining a second difference between acurrent value of a second angular coordinate of the tip and a desiredvalue of the second angular coordinate of the tip; and determining asecond product of the second difference and a second gain factor,wherein the second gain factor is set to be different from the firstgain factor.
 15. The system of claim 10, wherein determining the tipforce comprises: determining a difference between a component of acurrent velocity of the tip and a component of a desired velocity of thetip; determining a product of the difference and a gain factor; andusing the product in determining a component of the tip force.
 16. Thesystem of claim 10, wherein determining the tip force comprises:determining a difference between an angular velocity of the tip and adesired angular velocity of the tip; determining a product of thedifference and a gain factor; and using the product in determining acomponent of the tip force.
 17. The system of claim 10, wherein thejoints provide more than six degrees of freedom of motion, includingdegrees of freedom of motion that are redundant for movement of the tip,and the joint torques are computed to keep the joints away from limitsof ranges of motion of the joints or away from joint torque limits. 18.The system of claim 1, wherein the control system determines thetensions using a process comprising: using the configurationmeasurements to determine joint torques respectively in the joints; anddetermining the tensions for the transmission systems using the jointtorques.
 19. The system of claim 18, wherein the control systemdetermines the tensions using a process comprising: evaluating thejoints sequentially in an order from a distal end of the instrumenttoward a proximal end of the instrument, wherein evaluating each jointcomprises using the joint torques for that joint and tensions determinedfor joints closer to the distal end of the instrument to determinetensions directly applied to the joint being evaluated.
 20. The systemof claim 19, wherein when evaluating each joint, the tension of atransmission system directly applied to the joint being evaluated ischosen to be equal to a nominal value, and the tension or tensions ofthe remaining transmission systems directly applied to the joint arecomputed to produce the joint torques for that joint and are verified tobe greater than or equal to the nominal value.
 21. The system of claim20, wherein the nominal value is chosen to effectively release alltension in the transmission system.
 22. The system of claim 20, whereinthe nominal value is chosen to effectively keep tension in thetransmission systems.
 23. The system of claim 18, wherein determiningthe tensions using the joint torques comprises: determining distaltensions from the joint torques; and determining corrections that dependon respective differences between velocities of the joints andcorresponding velocities of the actuators coupled to the joints, whereinthe tensions for the transmission systems depend on the distal tensionsand the corrections.
 24. The system of claim 18, wherein determining thetensions using the joint torques comprises: determining distal tensionsfrom the joint torques; and determining for each joint a correction thatdepends on a difference between velocities of the actuators coupled totransmission systems that are attached to the joint, wherein thetensions for the transmission systems depend on the distal tensions andthe corrections.
 25. A method for controlling a medical instrument, themethod comprising: measuring a configuration for a plurality of jointsof the medical instrument; receiving a command indicating a desiredconfiguration of the medical instrument; determining tensionsrespectively in a plurality of transmission systems that respectivelyconnect a plurality of actuators to the joints, wherein determination oftensions is independent of positions of the actuators; and operating theactuator to apply the tensions respectively to the transmission systems.26. The method of claim 25, wherein one or more of the transmissionsystems has compliance such that each of those transmission systemsfails to provide a relationship between positions of the joint andpositions of the actuator coupled to the transmission system that issufficiently accurate for control of the joint using the relationship.27. The method of claim 25, wherein determining the tensions comprises:determining differences between a desired configuration of the jointsand a current configuration of the joints; determining from thedifferences joint torques that actuate the joints to reduce thedifferences; and determining the tensions that produce the jointtorques.
 28. The method of claim 25, wherein determining the tensionscomprises: determining differences between a desired configuration of atip of the instrument and a current configuration of the tip;determining from the differences a tip force and a tip torque that whenapplied to the tip reduces the differences; determining joint torquesthat produce the force and torque on the tip of the instrument; anddetermining the tensions that produce the joint torques.
 29. The methodof claim 28, wherein determining the tip force comprises: determining afirst difference between a current value of a first position coordinateof the tip and desired value of the first position coordinate of thetip; determining a first product of the first difference and a firstgain factor; and using the first product in determining a firstcomponent of the tip force.
 30. The method of claim 29, whereindetermining tip force further comprises: determining a second differencebetween a current value of a second position coordinate of the tip anddesired value of the second position coordinate of the tip; determininga second product of the second difference and a second gain factor,wherein the second gain factor is different from the first gain; andusing the second product in determining a second component of the tipforce.
 31. The method of claim 28, wherein determining the tip torquecomprises: determining a first difference between a current value of afirst angular coordinate of the tip and desired value of the firstangular coordinates of the tip; determining a first product of the firstdifference and a first gain factor; and using the first product indetermining a first component of the tip torque.
 32. The method of claim31, wherein determining the tip torque further comprises: determining asecond difference between a current value of a second angular coordinateof the tip and desired value of the second angular coordinate of thetip; and determining a second product of the second difference and asecond gain factor, wherein the second gain factor is set to bedifferent from the first gain factor.
 33. The method of claim 28,wherein determining the tip force comprises: determining a differencebetween a component of a current velocity of the tip and a component ofa desired velocity of the tip; determining a product of the differenceand a gain factor; and using the product in determining a component ofthe tip force.
 34. The method of claim 28, wherein determining the tipforce comprises: determining a difference between an angular velocity ofthe tip and a desired angular velocity of the tip; determining a productof the difference and a gain factor; and using the product indetermining a component of the tip force.
 35. The method of claim 28,wherein the joints provide more than six degrees of freedom of motion,including degrees of freedom of motion that are redundant for movementof the tip, and determining the joint torques uses the redundant degreesof freedom to keep the joints away from limits of ranges of motion ofthe joints or from joint torque limits.
 36. The method of claim 25,wherein determining the tensions comprises: using the configurationmeasurements to determine joint torques respectively in the joints; anddetermining the tensions for the transmission systems using the jointtorques.
 37. The method of claim 36, wherein determining the tensionsfurther comprises: evaluating the joints sequentially in an order from adistal end of the instrument toward a proximal end of the instrument,wherein evaluating each joint comprises using the joint torques for thatjoint and tensions determined for joints closer to the distal end of theinstrument to determine tensions directly applied to the joint beingevaluated.
 38. The method of claim 37, wherein when evaluating eachjoint, the tension of a transmission system directly applied to thejoint being evaluated is chosen to be equal to a nominal value, and thetension or tensions of the remaining transmission systems directlyapplied to the joint are computed to produce the joint torques for thatjoint and are verified to be greater than or equal to the nominal value.39. The method of claim 38, wherein the nominal value is chosen toeffectively release all tension in the transmission system.
 40. Themethod of claim 38, wherein the nominal value is chosen to effectivelykeep tension in the transmission systems.
 41. The method of claim 36,wherein determining the tensions comprises: determining distal tensionsfrom the joint torques; and determining corrections that depend onrespective differences between velocities of the joints andcorresponding velocities of the actuators coupled to the joints, whereinthe tensions for the transmission systems depend on the distal tensionsand the corrections.
 42. The method of claim 36, wherein determining thetensions using the joint torques comprises: determining distal tensionsfrom the joint torques; and determining for each joint a correction thatdepends on a difference between velocities of the actuators coupled totransmission systems that are attached to the joint, wherein thetensions for the transmission systems depend on the distal tensions andthe corrections.